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A support for the existence of paleolakes and paleorivers buried under Saharan sand by means of “gravitational signal” from EIGEN 6C4

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Abstract

The goal of this study is to demonstrate that and how the recent gravitational and topographic data support the findings made by geologists and others as for the existence of the paleolakes and paleoriver systems, now buried under the sands of Sahara. It is always important and useful to have such an independent analysis supporting certain results, and this paper is such a case. We make use of the gravity disturbances (or anomalies), the Marussi tensor of the second derivatives of the disturbing geopotential, the gravitational invariants and their certain ratio, the strike angle and the virtual deformations. The geopotential is represented by the global combined (from satellite and terrestrial data) high-resolution gravity field model EIGEN 6C4 (till degree and order 2160 in spherical harmonic expansion). The topography is derived from the ASTER GDEM and ETOPO 1 models (both are used). With all these data, we confirm the existence of huge paleolakes or paleoriver systems under the Saharan sands known or anticipated in an independent way by geologists for the lakes MegaChad, Fazzan and Chotts; for Tamanrasset river valley; and Kufrah Basin, presumptive previous flow of the Nile River. Moreover, we suggest a part of the Grand Egyptian Sand Sea as another “candidate” for a paleolake and hence for a follow-up survey.

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Acknowledgements

This work has been prepared in the frame of projects #13-36843S (Grant Agency of the Czech Republic) and RVO #679 858 15 (Czech Academy of Sciences), partly supported by the project LO 1506 (PUNTIS) from Ministry of Education of the Czech Republic. We are obliged to Ing. B. Bucha, PhD (STU Bratislava) for computations of the functions of the disturbing potential (here EIGEN 6C4) and Ing. Karolina Hanzalová for a part of topographic data.

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Authors and Affiliations

  1. Astronomical Institute, Czech Academy of Sciences, CZ 25 165 Ondřejov,, Fričova 298, Czech Republic

    Jaroslav Klokočník & Aleš Bezděk

  2. Research Institute of Geodesy, Topography and Cartography, CZ 25 066, Zdiby 98, Czech Republic

    Jan Kostelecký

  3. Geological Institute, Czech Academy of Sciences, CZ 165 00 Praha 6 – Lysolaje,, Rozvojová 269, Czech Republic

    Jan Kostelecký

  4. Department of Geomatics, Faculty of Civil Engineering, Czech Technical University in Prague, CZ 16 629, Praha 6 – Dejvice, Thákurova 7, Czech Republic

    Václav Cílek

  5. Faculty of Geology and Mining, TU Ostrava, CZ 708 36, Ostrava, Czech Republic

    Ivan Pešek

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  1. Jaroslav Klokočník
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Correspondence to Jaroslav Klokočník.

Appendix - artefacts

Appendix - artefacts

We recall sections “Gravitational field models with high resolution”, “Typical gravitational signal of various geological structures, note on artefacts” and “Lake MegaFazzan”. The method of solution for the harmonic geopotential coefficients is in fact a type of Fourier analysis. The input data are inevitably gridded (they are not continuous), and thus, the mathematical process generates “false” harmonic frequencies. As an example, let us take the function “sinus” defined on the interval <0°, 360°> by the individual data points given in an interval 20° (Fig. 16). After the Fourier transform, we receive a frequency spectrum shown in Fig. 17. Due to the gridding, we observe many frequencies and not the expected “theoretical” period of 360°. The most important frequencies, together with their amplitudes, are gathered into Table 2. By this way, we explain at least some of the artefacts discussed in sections “Typical gravitational signal of various geological structures, note on artefacts” and “Gravitational signal and topography for selected zones of Sahara with EIGEN 6C4 and ASTER GDEM”. Besides this, we can observe classical big “long-wave” aliasing effect (Fig. 18), originating when very few observations would be available in the interval <0°, 360°>. The artefacts depend on the density of the input data and on numerical precision of the transform.

Fig. 16
figure 16

The input data to Fourier analysis; data interval is 20°

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Fig. 17
figure 17

Output from the Fourier transform; the frequency spectrum with artefacts

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Fig. 18
figure 18

The well-known aliasing as a “long-wave” artefact. The long wave would constitute from the dots

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Table 2 The approximation of the function “sinus” on the interval <0°, 360°>. The most important frequencies, together with their amplitudes, after the Fourier transform of “sinus” function with the gridded input data
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Klokočník, J., Kostelecký, J., Cílek, V. et al. A support for the existence of paleolakes and paleorivers buried under Saharan sand by means of “gravitational signal” from EIGEN 6C4. Arab J Geosci 10, 199 (2017). https://doi.org/10.1007/s12517-017-2962-8

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